Recently, pictures taken by the New Horizons space probe were released depicting the unusually-shaped object Ultima Thule. Now, suppose there was an world the size of the Earth, but in the shape of Ultima Thule. What would the gravity be like, and if there were oceans, how would the water be distributed?

Also, this is assuming that this world were somehow able to maintain its shape instead of collapsing into itself.

$\begingroup$Whatever you’re changing in the laws of physics to permit the world to exist will also change the weather, oceans, gravity and so on. You’ll have to tell us what your physical laws are to get a meaningful answer.$\endgroup$
– Mike ScottJan 2 '19 at 21:23

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$\begingroup$This might not be answerable. How would such an object orbit a star? How would it rotate? Estimating the warming action of a sun on such an object is a PhD thesis all by itself. Estimating how a biome would develop is probably impossible (and too-broad for this site). So, let's say the Hand of God held the object, placed all the grass, atmosphere, oceans, rabbits, etc., started His stopwatch and let it go, orbiting and rotating a sun... even that answer might be too broad. Maybe if you can keep the question from being closed if you focus only on the oceans (just the water).$\endgroup$
– JBHJan 2 '19 at 21:28

$\begingroup$Earth-sized object of this shape would collapse to get into hydrostatic equilibrium, got really hot in the process, and then continue as alternate spherical Earth. Unless you describe magic that prevents this scenario, this will be the only "answer" you can get.$\endgroup$
– MołotJan 2 '19 at 22:20

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$\begingroup$@cmaster I expected OP to edit the question in a way that would invalidate such answer. That's why I posted as comment. Doesn't matter now, such answer is already posted.$\endgroup$
– MołotJan 3 '19 at 8:29

3 Answers
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This question is strongly related to this other , therefore I will reuse the answer I posted there:

The maximum height of a peak which can self sustain on the Earth surface is a bit more than the height of mount Everest.

The Moon diameter is way more than that. Therefore, assuming the mad scientist could really swiftly place the Moon on Earth, our satellite could not self sustain, and would spread on the surface. However, there are a couple of things to keep in mind:

it is the distance in which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.

For the Earth Moon the Roche limit is around 9500 km. This means that once the Moon gets closer than that to Earth, it would start break apart. The Scientist would have a hard time holding together the pieces falling from the Moon. The slightest failure would result in a meteor shower, which from 9000 km height would be quite energetic.

Momentum of inertia

Even assuming that the above could be avoided, the potatoid resulting from joining the Moon and the Earth would put the rotation of Earth off balance, resulting in quite some vibration while the system rearrange in a new equilibrium position.

Both of the above are highly unpleasant for those thiny things on Earth which we call "life forms", which, being close to the Moon, fall under your question

Summarizing, the gravity will prevent the thing to be stable, and will crumble it into a spheroid. The resulting heating will evaporate any water that should have the fortune of being present on the bodies.

Such a planetary system would be double locked and can share an atmosphere. Eventually they'll end up sharing ocean and land and over the course of geo-theiological time will form a peanut shaped roche world (such as Ultima Thule seems to be) and will eventually collapse into a larger single planet.

This is with an awful lot of assumptions which are not really viable by any science.

Assumption 1: You can "simply" scale it up (because Ultima Thule is guaranteed to be smaller)

Assumption 2: When scaled up Everything thats effecting the shape ignores the shape butworks outside of it as if nothing changed (not feasible to any extend in the real world)

Definitions:

North: The top end of the Object (when viewed from the Picture)

South: The bottom end of the Object (when viewed from the Picture)

Merge: The point where the two Parts meet

Gravity

Would change dramatically depending on how far away you are from the Merge as long as you are the same distance away from the merging point Gravity is consistent. (Assuming even density through out the Object)

There are two "peaks" in gravitational force one when on the south and one on the North although the north peak force is weaker than the south peak force. (because when in the south you are closer to more mass than when in the north. (Assuming same density for both Parts)

The lowest gravity is a little north of the Merge as the smaller part is closer and thereby pulls stronger per kg on the observer than the bigger part and can because of that cancel more force from the larger object out. It also could be that there is a point between the two parts where the gravitational pull is not towards the ground but to the left or the right of the observer. (Assuming left or right are defined by where the ground is and not where the gravitational pull pulls you toward)

Water

Water would pile up a bit to the south of the Merge. Anywhere else you would find only very small pockets of water (pond size) if at all.

Atmosphere

Atmosphere would behave similar to water with the difference being that you would probably find everywhere at least a little bit of atmosphere gases. Because of the uneven amount of atmosphere around the object pressure near the Merge would be way higher than anywhere else. (This would be counteracted to a degree by the lower gravitational pull near the Merge)

Live

The rings we see on our own earth because of difference in surface temperature would be way thinner and not only caused by the temperature difference but by the differences in atmospheric pressure and gravity.

When given rotation (and rotation speed) and distance from the star as well as star type(and age) I could give basic predictions about weather and flora/fauna.